No, IIT Delhi does not provide MA in English. Some other IITs do provide humanities programs, for instance, IIT Madras offers 5-year integrated MA courses in English as well as in Development Studies. Admission to these courses is done through an entrance test called HSEE.
Other IITs have their own net above tests for the specific humanities programs offered and details can be sought from the official website of respective colleges. Additionally, some IITs also offer Ph.D. programs in different humanities disciplines including English literature.